1. Field of the Invention
The present invention relates to an electron source and an image-forming apparatus such as a display apparatus as an application of the electron source and, more particularly, to a surface-conduction electron-emitting device having a new structure, an electron-emitting apparatus or an electron source using the surface-conduction electron-emitting device, and an image-forming apparatus such as a display apparatus as an application of the electron source.
2. Related Background Art
Electron-emitting apparatuses using surface-conduction electron-emitting devices have simple structures, and can be easily manufactured and driven by a driving voltage of several to several tens V. Recently, the electron-emitting apparatuses as flat-type display apparatuses have been developed and researched.
The structures and manufacturing methods for the surface-conduction electron-emitting device and the electron-emitting apparatus using the same have been described in detail in, e.g., Japanese Patent Application Laid-Open No. 7-235255. This prior art will be briefly described below.
FIGS. 1A and 1B are schematic views of a conventional surface-conduction electron-emitting device. FIG. 1A is a plan view of the device, and FIG. 1B is a side view of the device. The device includes a substrate 1, a positive device electrode 2, and a negative device electrode 3 and is connected to a power supply (not shown). Electroconductive films 5004 and 5005 are electrically connected to the positive device electrode 2 and the negative device electrode 3, respectively. The thicknesses of the electrodes 2 and 3 are several tens nm to several .mu.m. The thicknesses of the electroconductive films 5004 and 5005 are about 1 nm to several tens nm. A fissure 5006 almost electrically disconnects the electroconductive film 5004 from the electroconductive film 5005. The characteristic features of the fissure will be described together with the manufacturing process. After the device is formed, electrons are scattered and emitted from a portion near the distal end portion of the electroconductive film on the positive device electrode side of the fissure 5006.
An electron-emitting apparatus using the surface-conduction electron-emitting device will be described below with reference to FIG. 2.
FIG. 2 is a schematic view showing the electron-emitting apparatus using the surface-conduction electron-emitting device having the structure shown in FIGS. 1A and 1B.
This apparatus includes a power supply 10 for applying a device voltage V.sub.f to the device, an ammeter 11 for measuring a device current I.sub.f flowing across the device electrodes 2 and 3, an attracting electrode 12 for capturing electrons emitted from the electron-emitting portion of the device, a high-voltage power supply 13 for applying a voltage V.sub.a to the attracting electrode 12, and an ammeter 14 for measuring an emission current I.sub.e generated by electrons emitted from the surface-conduction electron-emitting device and arriving at the attracting electrode. Additionally, a mesh electrode or phosphor plate is attached to the attracting electrode 12 to measure the distribution of electron arrival positions, as needed. To emit electrons, the power supply 10 is connected to the device electrodes 2 and 3, and the power supply 13 is connected to the electron-emitting device and the attracting electrode 12. To measure the device current I.sub.f and the emission current I.sub.e, the ammeters 11 and 14 are connected, as shown in FIG. 2.
The surface-conduction electron-emitting device and the attracting electrode are set in a vacuum vessel 16, as shown in FIG. 2, such that the voltages applied to the device and the electrode can be controlled outside the vacuum vessel. An exhaust pump 15 is constituted by a normal high-vacuum exhaust system comprising a turbo pump and a rotary pump, and an ultra high-vacuum exhaust system comprising an ion pump. The entire vacuum vessel 16 and the electron-emitting device substrate can be heated by a heater (not shown).
The device voltage V.sub.f can change within the range of about zero to several tens V, and the voltage V.sub.a of the attracting electrode can change within the range of zero to several kV. A distance H between the attracting electrode and the electron-emitting device is set on the order of several mm.
A method of manufacturing the surface-conduction electron-emitting device will be described below with reference to FIGS. 3A to 3C.
Step-a
A silicon oxide film having a thickness of about 0.5 .mu.m is formed on a cleaned soda-lime glass by sputtering, and a photoresist pattern (negative pattern) of the device electrodes 2 and 3 is formed on the substrate 1. A Ti film having a thickness of, e.g., 5 nm and an Ni film having a thickness of 100 nm are sequentially deposited on the resultant structure by vacuum deposition. The photoresist pattern is dissolved by an organic solvent. The Ni and Ti deposition films are lifted off to form the device electrodes 2 and 3 (FIG. 3A).
Step-b
A Cr film having a thickness of about 100 nm is deposited by vacuum deposition and patterned by photolithography to form an opening conforming to an electroconductive film. An organic Pd compound (ccp4230, available from Okuno Seiyaku K.K.) is rotatably applied by a spinner, and a heating and baking treatment is performed to form an electroconductive film 7 formed of fine particles whose principal ingredient is palladium oxide. The film of fine particles is a film consisting of a plurality of fine particles. As for the fine structure, the fine particles are not limited to dispersed particles. The film may also be a film comprising fine particles arranged to be adjacent to each other or overlap each other (an island structure is also included).
Step-c
The Cr film is etched using an acid etchant and lifted off to form the desired pattern of the electroconductive film 7 (FIG. 3B).
Step-d
The device is set in the apparatus shown in FIG. 2. The apparatus is evacuated by the vacuum pump to a degree of vacuum of about 2.7.times.10.sup.-3 Pa (2.times.10.sup.-5 Torr). The power supply 10 for applying the device voltage V.sub.f to the device applies the voltage across the device electrodes 2 and 3 to perform electrification process called energization forming. This energization forming process is performed by applying a pulse voltage with a constant or gradually stepping up pulse height. With this energization forming process, the electroconductive film 7 is locally destroyed, deformed, or changed in properties, thus forming the fissure 5006 (FIG. 3C). Simultaneously, a resistance measurement pulse is inserted between the energization forming pulses at a voltage of, e.g., 0.1 V not to locally destroy or deform the electroconductive film 7 during energization forming, thereby measuring the resistance. When the measured resistance of the electroconductive film 7 becomes about 1 M.OMEGA. or more, application of the voltage to the device is stopped to end the energization forming.
Step-e
The device which has undergone the energization forming is preferably subjected to processing called activation. With the activation processing, the device current I.sub.f and the emission current I.sub.e largely change. The activation processing can be performed by repeating pulse application in an atmosphere containing, e.g., the gas of an organic substance, as in energization forming. This atmosphere can be obtained using an organic gas remaining in the atmosphere in evacuating the vacuum vessel by using, e.g., an oil diffusion pump or rotary pump, or supplying an appropriate gas of an organic substance into the vacuum obtained by sufficiently evacuating the vacuum vessel using an ion pump or the like. The preferable gas pressure of the organic substance changes depending on the application form, the shape of the vacuum vessel, or the type of organic substance, and is appropriately set in accordance with the situation. Examples of the appropriate organic gas are aliphatic hydrocarbons such as alkane, alkene, and alkyne, aromatic hydrocarbons, alcohols, aldehydes, ketones, amines, phenols, organic acids such as carboxylic acid and sulfonic acid. More specifically, a saturated hydrocarbon represented by C.sub.n H.sub.2n+2 such as methane, ethane, or propane, an unsaturated hydrocarbon represented by C.sub.n H.sub.2n such as ethylene or propylene, benzene, toluene, methanol, ethanol, formaldehyde, acetaldehyde, acetone, methyl ethyl ketone, methylamine, ethylamine, phenol, formic acid, acetic acid, or propionic acid, or a mixture thereof can be used. With this process, carbon and/or a carbon compound resulting from the organic substance present in the atmosphere is deposited on the device, so that the device current I.sub.f and/or the emission current I.sub.e largely changes. The end of the activation processing is appropriately determined while measuring the device current I.sub.f and the emission current I.sub.e. The pulse width, the pulse interval, and the pulse height are appropriately set. Carbon and/or a carbon compound means e.g., graphite (graphite contains so-called HOPG, PG, or GC; HOPG is an almost perfect graphite crystal structure, and PG is a slightly disordered crystal structure having crystalline grains of about 20 nm, while GC contains crystal grains having a size as small as 2 nm and has a crystal structure that is remarkably in disarray) or non-crystalline carbon (non-crystalline carbon means amorphous carbon or a mixture of amorphous carbon and fine crystal of graphite). The thickness of carbon and/or carbon compound is preferably 50 nm or less, and more preferably, 30 nm or less. By depositing the carbon compound, the effective width of the fissure decreases so that electrons are scattered and emitted from the distal end of the electroconductive film on the positive device electrode side. When the electron emission positions in the resultant device are averaged along the fissure at a measure of 10 to 100 nm, the electron emission positions are continuously distributed along the fissure, as is known. That is, the electron emission points are almost continuously and uniformly present at a resolution of 10 to 100 nm.
The electron-emitting device obtained by the above processes is preferably subjected to a stabilization process. In the stabilization process, the organic substance in the vacuum vessel and on the device is removed. As the vacuum pump 15 for evacuating the vacuum vessel 16, a pump which uses no oil is preferably used to prevent the oil generated from the apparatus from affecting the device characteristics. More specifically, a vacuum exhaust apparatus such as a combination of a sorption pump and an ion pump can be used. When an oil diffusion pump or a rotary pump is used as the exhaust apparatus, and an organic gas from the oil component generated from the exhaust apparatus is used in the activation processing, the partial pressure of this component must be minimized. The partial pressure of the organic component in the vacuum vessel is preferably so low as not to newly deposit the carbon and/or carbon compound, e.g., 1.3.times.10.sup.-6 Pa (1.times.10.sup.-8 Torr) or less, and more preferably, 1.3.times.10.sup.-8 Pa (1.times.10.sup.-10 Torr) or less. When the vacuum vessel is to be evacuated, the entire vacuum vessel is preferably heated to easily remove the organic substance molecules adsorbed on the inner wall of the vacuum vessel or the electron-emitting device. The heating is preferably performed at 80.degree. C. to 250.degree. C., and more preferably, 150.degree. C. or more for a time as long as possible. However, the heating condition is not limited to this. Heating is performed under a condition appropriately selected in accordance with various conditions including the size and shape of the vacuum vessel and the structure of the electron-emitting device. The pressure in the vacuum vessel must be minimized and is preferably 1.3.times.10.sup.-5 Pa (1.times.10.sup.-7 Torr) or less, and more preferably, 1.3.times.10.sup.-6 Pa (1.times.10.sup.-8 Torr) or less. As an atmosphere for driving the device, the atmosphere at the end of the stabilization process is preferably maintained. However, the atmosphere is not limited to this. As long as the organic substance is sufficiently removed, sufficiently stable characteristics can be maintained although the degree of vacuum itself slightly decreases. By employing this vacuum atmosphere, new deposition of carbon and/or carbon compound can be prevented, and H.sub.2 O or O.sub.2 adsorbed on an inner wall of the vacuum vessel or the substrate of the device also be removed, thus stabilizing the device current I.sub.f and the emission current I.sub.e.
The basic characteristics of the electron-emitting apparatus having the above-described device structure and prepared by the above manufacturing method will be described with reference to FIG. 4. FIG. 4 shows the typical relationship among the emission current I.sub.e, the device current I.sub.f, and the device voltage V.sub.f measured by the electron-emitting apparatus shown in FIG. 2. FIG. 4 is illustrated using arbitrary units because the emission current I.sub.e is much smaller than the device current I.sub.f. All axes are represented by linear scales.
As is apparent from FIG. 4, the electron-emitting apparatus has three characteristics for the relationship between the emission current I.sub.e and the device voltage V.sub.f. First, when a device voltage equal to or higher than a certain voltage (to be referred to as a threshold voltage hereinafter: V.sub.th in FIG. 4) is applied to the device, the emission current I.sub.e abruptly increases. When the applied voltage is lower than the threshold voltage V.sub.th, almost no emission current I.sub.e is detected. That is, this device is a nonlinear device having the clearly defined threshold voltage V.sub.th with respect to the emission current I.sub.e. Second, since the emission current I.sub.e depends on the device voltage V.sub.f, the emission current I.sub.e can be controlled by the device voltage V.sub.f. Third, the amount of arriving charges captured by the attracting electrode 12 depends on the time for which the device voltage V.sub.f is applied. That is, the amount of charges captured by the attracting electrode 12 can be controlled by the time for which the device voltage V.sub.f is applied.
According to the above-described characteristics, at a voltage equal to or higher than the threshold voltage, electrons captured by the attracting electrode 12 are controlled by the pulse height and width of the pulse voltage applied across the opposing device electrodes. At a voltage lower than the threshold voltage, almost no electrons reach the attracting electrode. Even when a number of electron-emitting devices are arranged, the surface-conduction electron-emitting devices can be selected in accordance with an input signal by appropriately applying the pulse voltage to the individual devices, so that the electron emission amount can be controlled.
When a plurality of electron-emitting apparatuses are constituted on the basis of this principle, a flat-type image display apparatus can be formed. The constituting method is disclosed in detail in Japanese Patent Application Laid-Open No. 7-235255. This will be briefly described. A plurality of surface-conduction electron-emitting devices are arranged on the same substrate in correspondence with the pixels of a flat-type image display apparatus. Wires from the device electrodes 2 and 3 are arrayed in a simple matrix as row-directional and column-directional wires. As the attracting electrode, a common electrode is used. Phosphor films are applied on the attracting electrode at positions corresponding to the electron-emitting devices, thereby forming pixels. The pixels can be turned on by electrons attracted by the attracting electrode. In driving, a positive potential V (V.sub.th &gt;V&gt;V.sub.th /2) is selectively applied to the row-directional wires, and a negative potential -V (V.sub.th &gt;V&gt;V.sub.th /2) is selectively applied to the column-directional wires. With this operation, only selected devices along the rows and columns are applied with a device voltage higher than the threshold voltage V.sub.th. On the basis of this fact and the above-described characteristics of the electron-emitting apparatus using the surface-conduction electron-emitting device, only the selected devices along the rows and columns can be driven.
In addition to the above-described electron-emitting apparatus using the general surface-conduction device, the following invention has been applied. A surface-conduction electron-emitting device in which the positive device electrode and the negative device electrode are not symmetrical is proposed in Japanese Patent Application Laid-Open Nos. 1-311532, 1-311533, and 1-311534. In Japanese Patent Application Laid-Open Nos. 1-311532, 1-311533, and 1-311534, the object is to shape an electron beam arriving at the attracting electrode. The present invention is to solve a problem different from that of the prior arts, as will be described later.
In the flat-type display apparatus according to the principle of the electron-emitting apparatus described in the prior art, an efficiency .eta. (.eta.=I.sub.e /I.sub.f) corresponding to the ratio of the emission current amount I.sub.e of electrons arriving at the attracting electrode 12 to the device current amount I.sub.f is preferably high. More specifically, when the efficiency .eta. can be raised, the device current I.sub.f necessary for obtaining the same emission current I.sub.e can be decreased. It can be expected that the wires for connecting the devices be easily designed, or degradation of devices be suppressed.
The problem to be solved by the present invention is to improve the efficiency of the electron-emitting apparatus while maintaining a constant current amount at the attracting electrode.
To describe this problem in more detail, the mechanism of the electron-emitting apparatus using the surface-conduction electron-emitting device will be described below.
As described above, with the process called energization forming and the process called activation, a fissure is formed in the electroconductive film of the surface-conduction electron-emitting device such that the electroconductive film is divided into a portion electrically connected to the positive device electrode and a portion electrically connected to the negative device electrode. It is found that, of this fissure in the film, a portion having a width of nm order is present. In addition, various examination experiments and computer simulations reveal that electrons are almost isotopically emitted from the distal end portion of the higher potential-side film neighboring the portion of the fissure of nm order (exactly, assuming that electrons are isotopically emitted from the distal end portion of the higher potential-side film portion, the experimental results coincide with the simulation results without any contradiction). The higher potential-side film portion is an electrically connected portion which can be regarded as an equipotential portion including the electroconductive film 5004 and the positive device electrode 2. Similarly, a portion which can be regarded as an equipotential portion including the electroconductive film 5005 and the negative device electrode 3 will be referred to as a lower potential-side film portion hereinafter.
By examining the motion of electrons in an electrostatic field, it is found that the electrons emitted from the distal end of the higher potential-side film portion exhibit behavior different from those emitted from the negative device electrode side as in a field-emission electron-emitting device. The characteristic motion of electrons in the electron-emitting apparatus using the surface-conduction electron-emitting device will be examined below.
The fissure in the actual surface-conduction electron-emitting device has an irregular zigzag shape. The amplitude of the zigzag fissure is often almost 1/2 or less the width between the positive device electrode and the negative device electrode although it depends on the device formation method or the like. Therefore, a theory must be constituted in consideration of the zigzag fissure. For the descriptive convenience, a device having a zigzag fissure with a minimum amplitude and a theoretical model corresponding to this device will be described first. That is, an electrostatic potential distribution for a linear fissure will be described. FIGS. 5A to 5C are sectional views of potential distributions of various orders. (After examination of the motion of electrons for the linear fissure, that for the zigzag the fissure will be examined in detail, and the problem for the present invention will be described).
Assume that a fissure 30 portion is a linear fissure, and the surfaces of the device electrodes and the film portions are on a plane where z=0 and extend to have a sufficiently larger area than a given region (a region 34 in FIG. 6; to be described later in detail). When the potential distribution can be regarded to be completely binarized on a higher potential-side film portion 31 and a lower potential-side film portion 32, the higher potential-side film portion 31 and the lower potential-side film portion 32 can be electrostatically approximated as two opposing electrode plates. When the distance H between the device and the attracting electrode 12 is sufficiently large as compared to the given region 34, the field distribution (E.sub.x, 0, E.sub.z) in the electron-emitting apparatus using the surface-conduction electron-emitting device is given by equation (1) while regarding the (x,y) plane as a complex plane:
Equation (1) ##EQU1## where i=.sqroot.-1, and .pi. is the circle ratio. The center of the coordinates is set at the center of the fissure, and D is the effective fissure width. V.sub.f is the voltage applied to the device within the range of several to several tens V. V.sub.a is the voltage applied across the device and the attracting electrode within the range of several to several tens kV. The distance H between the device and attracting electrode is on the order of several mm. Therefore, V.sub.a /H is on the order of about 10.sup.6 to 10.sup.7 V/m.
The effective width D means a width as a parameter fitted to equation (1) such that the width matches the actual electric field at a position separated from the center of the fissure by a distance several tens times the size of the fissure. As is experimentally known, this width is on the order of several nm in the surface-conduction electron-emitting device.
FIGS. 5A to 5C show potential distributions obtained by integrating the electric field described by equation (1) by various scales. FIG. 5A shows the potential distribution of mm order. FIG. 5B shows the potential distribution of .mu.m order. FIG. 5C shows the potential distribution of nm order. (The fissure, the higher potential-side film portion, the lower potential-side film portion, and the attracting electrode 12 which are approximated by equation (1) will be represented by 30, 31, 32, and 33, respectively, and corresponding portions are shown in FIGS. 5A to 5C).
The electric field becomes zero on a straight line parallel to the fissure (Y-axis) on the plane where z=0, in which the value x is given by equation (2) below:
Equation (2) ##EQU2## When the potential is regarded as the imaginary part of a complex fluid potential, a point where the flow field stagnates corresponds to the field zero point because of the nature of the potential as a harmonic function. On the basis of the analogy between the fluid and the electrostatic field, the linear portion where the electric field stagnates will be referred to as a stagnation line, or a stagnation point 35 based on the sectional shape of the (x,z) plane. A distance x.sub.s from the center of the fissure to the stagnation point 35 is a length representing the characteristic feature of this system.
On the order in the electron-emitting apparatus, x.sub.s &gt;&gt;D, and x.sub.s can be sufficiently approximated as equation (3):
Equation (3) ##EQU3## As is apparent from equation (3), x.sub.s does not depend on the effective width D (x.sub.s &gt;&gt;several nm). When V.sub.a is 1 kV, V.sub.f is 15 V, and H is 5 mm, x.sub.s is about 23.9 .mu.m.
The approximation of equation (3) corresponds to field distribution approximated as equation (4) below:
Equation (4) ##EQU4## When the ratio of x.sub.s to the fissure width is sufficiently high, i.e., in a region outside a semicircular cylinder having a radius of several times the effective fissure width D from the center of the fissure 30, this approximation is a good approximation. The first term on the right side of equation (4) represents a so-called revolving field. The second term represents an electric field called a longitudinal field. The characteristic field in the electron-emitting apparatus using the surface-conduction electron-emitting device can be approximated by the sum of the revolving field and the longitudinal field.
The potential distribution corresponding to equation (4) is obtained by integrating equation (4) as equation (5):
Equation (5) ##EQU5## where Im represents the imaginary part.
Analysis of the electric field given by equation (1) shows that a region where the electric field has a vector component in the positive direction of the Z-axis is present in the higher potential-side film portion 31. The region has a solid semicircular cylindrical shape obtained by translating, along the Y-axis, an almost semicircular region having a radius 1/2 x.sub.s while setting the central axis at the center of the fissure 30 and the center of the stagnation point 35. In this region, electrons receive a downward force. This region will be referred to as a negative gradient region 36 hereinafter. The corresponding region is indicated as a hatched portion in FIG. 5B. When approximation of equation (4) holds, the negative gradient region 36 is surrounded by a perfect semicircle and the X-axis on the Z-X plane.
Even when electrons are emitted from the distal end portion of the higher potential-side film portion 31 by a certain effect, the electrons fall in the negative gradient region 36 upon receiving the downward force (in the negative direction of the Z-axis in FIG. 5B). In addition, various analyses reveal that the electrons fall onto the surface of the higher potential-side film portion 31, some electrons are absorbed into the higher potential-side film portion 31 and flow as the device current, and some other electrons are scattered into the vacuum again. The electrons are emitted from the distal end portion of the higher potential-side film portion 31, and then repeatedly fall and scatter. Only electrons completely passing through the negative gradient region 36 reach the attracting electrode 33 and become the emission current.
When the lengths of the higher potential-side film portion 31 and the lower potential-side film portion 32 along the X direction are larger than x.sub.s, the film portions can be regarded as opposing electrode plates, as in the above approximation. When the scale of the zigzag fissure is much smaller than x.sub.s, the fissure can be regarded as a linear fissure.
In the above sense, the fissure in the surface-conduction electron-emitting device can be regarded as a linear fissure. The above-described "given region" is a parallelepiped cylindrical region extending along the Y direction and having a height of several to several tens times x.sub.s from the device surface in the Z direction, at which electrons are present, and having a size of twice to ten times the stagnation point in the X direction. That is, 1) the fissure portion can be regarded as a linear fissure when the width of the meander is smaller than x.sub.s, 2) the unevenness of a surface of the portion of the films and electrodes of the device are much smaller than x.sub.s, 3) the higher potential-side film portion and the lower potential-side film portion extend across a sufficiently larger area than the region enclosed in the parallelepiped cylinder, and 4) when H&gt;&gt;x.sub.s holds, the system can be considered to have a field distribution described by equation (1) or (4). The electron-emitting apparatus using the general surface-conduction electron-emitting device almost satisfies the above conditions.
Electrons passing through the region enclosed in the parallelepiped cylinder exhibit a motion which can be regarded as an almost parabolic motion due to the parallel field shown in FIG. 5A between the device and the attracting electrode 33.
The field distribution approximated by equation (1) or (4) has a nature different from that in the electron-emitting apparatus in which the capture electrode corresponding to the attracting electrode 33, and electrodes corresponding to the equipotential portions 31 and 32 are formed on the same substrate. When the value of the voltage applied to the device is large, e.g., when V.sub.f is 200 V, V.sub.a is 1 kV, and H is 5 mm, x.sub.s is about 300 .mu.m. To form the device described by equation (1) or (4), a device of mm order must be considered. Therefore, when the value of the voltage applied to the device is large, and the device size is on the order of submillimeter or less, it can be easily estimated that the device has a field distribution different from the characteristic field distribution of the above-described surface-conduction electron-emitting device.
Almost all the characteristic features of the electrostatic system have been described above. The relationship between the motion of electrons and the electrostatic structure of this system will be described below.
Because of the energy conservation law, the energy of electrons emitted from the device (into the vacuum) is given by (eV.sub.f -W.sub.f) where e is the charges of electrons, and W.sub.f is the averaged work function on the surface of the higher potential-side film portion 31. Since V.sub.f is several to several tens V, and the work function is about 5 eV or so, for general material, the electrons have an energy of several to several tens eV. Electrons having the energy of several to several tens eV have a nature different from those having a high energy, as is known, although the details of the nature have not been clarified. As is apparent from various examinations, elastic scattering occurs on the surface of the higher potential-side film portion 31. When the entire ratio of the elastic scattering components is represented by .beta., the value .beta. is about 0.1 to 0.5. In addition, since the electrons exhibit a wave-like behavior in terms of quantum theory because of their low energy, and the film surface has three-dimensional patterns (unevenness), there are isotopically scattering components. Therefore, it is classically interpreted that the ratio of components which are scattered in a certain direction seems to be probabilistically given.
Because of such a scattering mechanism, it can be understood that the motion of electrons must be statistically handled. In addition, since the value .beta. is less than 1, it is found that electrons in the vacuum decrease by the power of the value .beta. every time the scattering is repeated.
Such multiple scattering is considered to decrease the efficiency .eta.(=I.sub.e /I.sub.f). Therefore, as a means for improving the efficiency, the number of times of falling of electrons onto the surface of the higher potential-side film portion 31 must be decreased.
As described above, the surface-conduction electron-emitting device having the linear fissure 30 absolutely has the negative gradient region 36 having an almost semicircular shape, and this negative gradient region 36 contributes to falling of electrons onto the surface of the higher potential-side film portion 31. Therefore, control of this negative gradient region 36 is the most important challenge.
In the above description, however, the degree of reduction of the negative gradient region 36, and the comparison target to which the size of the negative gradient region 36 is relatively reduced are obscure. The characteristic length of this system, which is determined by the energy of electrons, will be described next. This length is determined by the motion of electrons.
In the negative gradient region 36 and near the fissure 30, the electric field can be regarded as a revolving field by primary approximation. The motion of electrons associated with the revolving field at V.sub.a =0 has been analyzed by equation (4). As a result, it is found that when the Y-direction distribution of points where electrons isotopically emitted from a point (x.sub.0,0,0) on the higher potential-side film portion 31 fall onto on the higher potential-side film portion 31 is integrated, the distribution is almost represented by the following function by simulation:
Equation (6) ##EQU6## where N is the normalization constant, g.sub.0 is the positive monotonously increasing function, and C is the magnification parameter represented by equation (7) below:
Equation (7) ##EQU7## That the orbits of electrons are determined only by the magnification at the emission position means that, when V.sub.a is 0, the characteristic length is not present in this system. The maximum arrival position is also determined by the multiple of the emission position from the central portion of the fissure. Therefore, it can be considered that the emitted or scattered electrons rise at maximum to the height (in the positive direction of the Z-axis) on the order of:
Expression (8) EQU Cx.sub.0
When V.sub.f is 14 V, and W.sub.f is 5.0 eV, C is 130. When x.sub.0 is 5 nm, Cx.sub.0 is about 650 nm.
When the length determined by the motion of electrons is known, the comparison target to which the relative size of the negative gradient region 36 must be determined is obvious. That is, the negative gradient region 36 is not so large as compared with Cx.sub.0.
The effect of the zigzag fissure will be examined below. From the above examination, when the simplified electric field (1) is further approximated, the equation (1) can be rearranged as equation (4). Since the electrons undergo the probabilistic process, i.e., scattering, the calculation shows that the set of the orbits of electrons has a distribution at almost the same density as that obtained by equation (1) and in the electric field of equation (4). (In equation (6), the effect depending on the presence/absence of the effective fissure width D, and the like are calculated. As is known, when the fissure width is sufficiently smaller than x.sub.s the orbits of electrons are not largely affected by the presence/absence of the fissure width D. This condition is satisfied in the conventional electron-emitting apparatus). It can be understood that the electric field of equation (4) for the sufficiently small effective fissure width D (D=0) is the characteristic electric field of the electron-emitting apparatus using the surface-conduction electron-emitting device. Therefore, it is important to examine the electric field formed by the device portion consisting of the higher potential-side film portion 31 and the lower potential-side film portion 32 and the attracting electrode 33 for the sufficiently small effective fissure width D (D=0).
Even for the zigzag fissure, the ratio (x.sub.s /H) of the maximum value of x.sub.s to the distance between the attracting electrode 33 and the device can be considered to be sufficiently small (H&gt;&gt;x.sub.s). This ratio can be approximated as the linear sum (superposition) of the electric field formed by the device portion consisting of the higher potential-side film portion 31 and the lower potential-side film portion 32 and the electric field formed by the attracting electrode 33 when no effective fissure width is present.
Even when the actual fissure has a non-zero width, the substantial portion of the electric field of the zigzag fissure is expected to be the field distribution of the device portion when the effective fissure width is sufficiently small (D=0).
Assuming that the potential of the lower potential-side film portion 32 is zero, calculation reveals that the potential distribution formed by the device portion having the zigzag fissure present on the two-dimensional plane and having the sufficiently small width (D=0) is proportional to the solid angle with respect to the higher potential-side film portion 31 because of the characteristics of the Green's function on the half-space. When the shape of the higher potential-side film portion 31 is represented by .LAMBDA., and the solid angle from a point (x,y,z) on the half-space where z&gt;0 with respect to the higher potential-side film portion 31 s represented by .OMEGA..sub..LAMBDA. (x,y,z), the potential at that point is given by equation (9) below:
Equation (9) ##EQU8## (When V.sub.a is 0, the potential sensed by electrons corresponds to the solid angle with respect to the higher potential-side film portion, as shown in FIG. 7). The electric field is obtained by direction-differentiating this potential. Even for the non-zero fissure width, equation (9) holds with good approximation when the effective fissure width D is sufficiently smaller than x.sub.s, as is apparent from the above examination.
Assuming that the fissure is formed on the X-Y plane where z=0, and along the Y-axis where (x,y,z)=(0,y,0), it can be easily confirmed that equation (9) returns to equation (5).
From the viewpoint of reduction of the negative gradient region, the relationship between equation (9) and the negative gradient region will be examined below. The negative gradient region can be understood as the dominant region of the revolving field formed by the electron-emitting device. More specifically, on the boundary line of the negative gradient region, the Z-direction component of the revolving field balances the longitudinal field formed by the attracting electrode 33, and the revolving field is dominant in this region. Assuming that the potential of the lower potential-side film portion 32 is zero, the equipotential line (plane) of the value V.sub.f starts from the stagnation point (line) and becomes parallel to the X-Y plane at a position sufficiently separated from the fissure to the lower potential-side film portion 32. When a region inside (on the side including the fissure) of the equipotential line (plane) of V.sub.f is called a device potential region, it can be easily understood that the negative gradient region is confined in the device potential region. This nature does not depend on whether or not the fissure is a linear fissure.
The negative gradient region 36 can be made small by reducing the device potential region. FIGS. 8A to 8D show actually formed characteristic potentials. FIGS. 8A and 8C are plan views of device models, in which the corresponding higher potential-side film portion and lower potential-side film portion are represented by 31 and 32, respectively. FIGS. 8B and 8D show potential distributions corresponding to the linear and zigzag fissures shown in FIGS. 8A and 8C, respectively, on the sections taken along the dotted lines in FIGS. 8A and 8C. A negative gradient region 40 enclosed by a line becomes small.
To reduce the device potential region, the area of the higher potential-side film portion 31 may be increased with respect to the orbits of electrons, as can be concluded from equation (9). However, in the conventional surface-conduction electron-emitting device, the zigzag fissure is not controlled, and the electron-emitting portion is not controlled, either, so this idea has not been put into practical use.
This will be described in more detail. For the descriptive convenience, the fissure in the conventional surface-conduction electron-emitting device is modeled. Examination will be made for a fissure as shown in FIG. 9A, in which partially linear portions of the fissure are periodically arranged. The longitudinal amplitude is about 10 .mu.m, and the period is about 20 .mu.m. The ratio of electrons emitted from the distal end of the higher potential-side film portion and reaching the attracting electrode is calculated by computer simulation. In FIG. 9B, the abscissa represents the position, and the ordinate represents the efficiency. The straight line parallel to the abscissa represents the calculation result for a linear fissure. For Cx.sub.0 above the fissure, when a portion where the solid angle with respect to the higher potential-side film portion exceeds .eta. is present, a portion where the solid angle becomes smaller than .pi. is simultaneously generated. Reflecting this fact, at some portions, the efficiency exceeds that for the linear fissure and, at some other portions, the efficiency is lower than that for the linear fissure, as shown in the graph of FIG. 9B. For this reason, when portions where electrons are emitted are distributed along the fissure across the device portion, the average electron arrival ratio is almost the same as that for the linear fissure. When the amplitude and period are smaller than those for the zigzag fissure shown in FIG. 9A, the difference from the negative gradient region for the linear fissure effectively becomes small. The shape of the negative gradient region becomes closer to that for the linear fissure than that shown in FIG. 9A. Therefore, it can be estimated that the effect of the small zigzag fissure be neglected. Actually, such an effect was obtained by numerical experiment based on simulation.
As described above, when at least the amplitude of the zigzag fissure is relatively small, the negative gradient region becomes small at some portions although the negative gradient region simultaneously becomes large at some other portions. For this reason, for a simple zigzag fissure, the entire electron arrival ratio and the efficiency cannot be improved.